Space Mechanics Group,
Department of Mathematics, University of Pisa,
Via Buonarroti 2, I-56127 PISA, Italy
A small, but by no means negligible, fraction of the small bodies of the Solar System is on planet-crossing orbits, including Earth-crossing ones. The dynamics of planet-crossing asteroids/comets is strongly controlled by the occurrence of close approaches. The node crossing cycle, resulting from the secular evolution of the orbital elements, especially the argument of perihelion, is apparent in the evolution of all the elements, including the semimajor axis. The most common type of orbits defines the Geographos class, in which close approaches occur at random whenever they are made possible by the distance of the orbits. Other orbits are protected from close approaches either by mean motion resonances (Toro class) or by secular perturbations (Kozai class). The Alinda class is defined by the presence of a mean motion resonance with Jupiter, which can change over a comparatively short time the eccentricity and therefore the crossing behavior. In all cases the orbits are chaotic, and in the long run transitions between the different orbit types can occur. This paper summarizes the experimental evidence, resulting from numerical integrations, and the semianalytical theories (based upon the adiabatic invariant and upon the Kozai approximation) which can explain in a satisfactory way most of the dynamical behaviors found in the experiments.